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Modelling Lorenz curves: robust and semi-parametric issues

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  • Cowell, Frank
  • Victoria-Feser, M.P.

Abstract

Modelling Lorenz curves (LC) for stochastic dominance comparisons is central to the analysis of income distribution. It is conventional to use non-parametric statistics based on empirical income cumulants which are in the construction of LC and other related second-order dominance criteria. However, although attractive because of its simplicity and its apparent flexibility, this approach suffers from important drawbacks. While no assumptions need to be made regarding the data-generating process (income distribution model), the empirical LC can be very sensitive to data particularities, especially in the upper tail of the distribution. This robustness problem can lead in practice to “wrong” interpretation of dominance orders. A possible remedy for this problem is the use of parametric or semi-parametric models for the data-generating process and robust estimators to obtain parameter estimates. In this paper, we focus on the robust estimation of semi-parametric LC and investigate issues such as sensitivity of LC estimators to data contamination (Cowell and Victoria-Feser 2002), trimmed LC (Cowell and Victoria-Feser 2006) and inference for trimmed LC (Cowell and Victoria-Feser 2003), robust semi-parametric estimation for LC (Cowell and Victoria-Feser 2007) selection of optimal thresholds for (robust) semi-parametric modelling (Dupuis and Victoria-Feser 2006) and use both simulations and real data to illustrate these points.

Suggested Citation

  • Cowell, Frank & Victoria-Feser, M.P., 2007. "Modelling Lorenz curves: robust and semi-parametric issues," LSE Research Online Documents on Economics 2694, London School of Economics and Political Science, LSE Library.
  • Handle: RePEc:ehl:lserod:2694
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    References listed on IDEAS

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    1. McDonald, James B, 1984. "Some Generalized Functions for the Size Distribution of Income," Econometrica, Econometric Society, vol. 52(3), pages 647-663, May.
    2. Chiaki Moriguchi & Emmanuel Saez, 2006. "The Evolution of Income Concentration in Japan, 1886-2002: Evidence from Income Tax Statistics," NBER Working Papers 12558, National Bureau of Economic Research, Inc.
    3. Frank A. Cowell & Maria-Pia Victoria-Feser, 2002. "Welfare Rankings in the Presence of Contaminated Data," Econometrica, Econometric Society, vol. 70(3), pages 1221-1233, May.
    4. A. B. Atkinson, 2004. "Income Tax and Top Incomes over the Twentieth Century," Hacienda Pública Española, IEF, vol. 168(1), pages 123-141, march.
    5. Frank Cowell & Maria-Pia Victoria-Feser, 2003. "Distribution-Free Inference for Welfare Indices under Complete and Incomplete Information," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 1(3), pages 191-219, December.
    6. Kopczuk, Wojciech & Saez, Emmanuel, 2004. "Top Wealth Shares in the United States, 1916-2000: Evidence From Estate Tax Returns," National Tax Journal, National Tax Association;National Tax Journal, vol. 57(2), pages 445-487, June.
    7. Frank Cowell & Maria-Pia Victoria-Feser, 2007. "Robust stochastic dominance: A semi-parametric approach," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 5(1), pages 21-37, April.
    8. Emmanuel Saez & Michael R. Veall, 2005. "The Evolution of High Incomes in Northern America: Lessons from Canadian Evidence," American Economic Review, American Economic Association, vol. 95(3), pages 831-849, June.
    9. Cowell, Frank A. & Victoria-Feser, Maria-Pia, 2006. "Distributional Dominance With Trimmed Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 291-300, July.
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    JEL classification:

    • J1 - Labor and Demographic Economics - - Demographic Economics

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